The thermodynamic limit of the Whitham equations
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Publication:1870441
DOI10.1016/S0375-9601(03)00515-2zbMath1038.82029arXivnlin/0310014OpenAlexW3099481883MaRDI QIDQ1870441
Publication date: 13 May 2003
Published in: Physics Letters. A (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/nlin/0310014
KdV equations (Korteweg-de Vries equations) (35Q53) Soliton equations (35Q51) Kinetic theory of gases in equilibrium statistical mechanics (82B40)
Related Items (31)
Introduction to the Special Issue on Emergent Hydrodynamics in Integrable Many-Body Systems ⋮ Kinetic equation for soliton gas: integrable reductions ⋮ Whitham systems and deformations ⋮ Current correlations, Drude weights and large deviations in a box–ball system ⋮ Kinetic theory of quantum and classical Toda lattices ⋮ Generalized hydrodynamic reductions of the kinetic equation for a soliton gas ⋮ Critical density of a soliton gas ⋮ Generalized hydrodynamic limit for the box-ball system ⋮ Reductions of kinetic equations to finite component systems ⋮ Soliton–mean field interaction in Korteweg–de Vries dispersive hydrodynamics ⋮ Soliton versus the gas: Fredholm determinants, analysis, and the rapid oscillations behind the kinetic equation ⋮ Dispersive hydrodynamics of soliton condensates for the Korteweg-de Vries equation ⋮ Hamiltonian systems of Jordan block type: Delta-functional reductions of the kinetic equation for soliton gas ⋮ Partial degeneration of finite gap solutions to the Korteweg–de Vries equation: soliton gas and scattering on elliptic backgrounds ⋮ On classical integrability of the hydrodynamics of quantum integrable systems ⋮ A geometric viewpoint on generalized hydrodynamics ⋮ Kinetic equation for a soliton gas and Its hydrodynamic reductions ⋮ Soliton spectra of random water waves in shallow basins ⋮ Two-soliton interaction as an elementary act of soliton turbulence in integrable systems ⋮ Statistical equilibrium of the Korteweg–de Vries and Benjamin–Ono unidirectional soliton models ⋮ On minimal energy solutions to certain classes of integral equations related to soliton gases for integrable systems* ⋮ Rule 54: exactly solvable model of nonequilibrium statistical mechanics ⋮ Generalized hydrodynamics of the classical Toda system ⋮ Diffusion and superdiffusion from hydrodynamic projections ⋮ \(T\overline{T}\) deformations and the width of fundamental particles ⋮ Soliton gas in integrable dispersive hydrodynamics ⋮ Generalized hydrodynamics of the KdV soliton gas ⋮ Generalized hydrodynamics in box-ball system ⋮ The GGE averaged currents of the classical Toda chain ⋮ Recent developments in spectral theory of the focusing NLS soliton and breather gases: the thermodynamic limit of average densities, fluxes and certain meromorphic differentials; periodic gases ⋮ Hydrodynamic projections and the emergence of linearised Euler equations in one-dimensional isolated systems
Cites Work
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- Method of averaging for two-dimensional integrable equations
- The continuum limit of theta functions
- The small dispersion limit of the Korteweg-de Vries equation. III
- The korteweg-de vries equation with small dispersion: Higher order lax-levermore theory
- The Zero Dispersion Limit of the Korteweg-de Vries Equation With Periodic Initial Data
- Asymptotic Behavior of Stability Regions for Hill’s Equation
- Non-linear dispersive waves
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